Evaluating the stabilities of common power-law models for describing particle size distributions across the continental shelf of the northern South China Sea

The accurate initial background of the high heterogeneity of particle size distributions (PSDs) is crucial for modeling the carbon cycle across the continental shelf. However, the lack of field measurements and constraints on PSDs has made this task challenging. In particular, different power-law models have been used to fit field PSDs, which can introduce bias in the calculated PSD slopes (xi s) and mislead subsequent biogeochemical modeling. This study analyzes the characteristics and variabilities of PSDs across the continental shelf of the northern South China Sea (NSCS) using field data and evaluates the stability of common power-law models for calculating xi. The first-order variations of most regional PSDs follow the power-law distributions. However, the second-order variations of these PSDs lead to fluctuations in xi values calculated by the different-reference-point power-law model, which lacks a correction parameter. A power-law model with a correction factor can be used to calculate xi stably, regardless of the second-order variations of these PSDs. We recommend using this power-law model to calculate xi, and it can be extended to describe other oceanic field PSDs. Our results also highlight the high spatial heterogeneity of xi across the NSCS continental shelf, which should be considered in regional biogeochemical modeling. Our study provides important insights into which power-law model can be used to derive stable and comparable xi-field datasets for the purpose of initializing and constraining of biogeochemical models.